Quaternion Interpolation Under the Angular Velocity Constraint

In this paper we present a novel approach to interpolate the attitude. Quaternions are used to define the attitude for space vehicles and in some missions such as Earth imaging, considering the periodically incoming quaternion data, if an image is taken between two periods, obtaining the quaternion data of the relevant moment can only be found by interpolating the previous quaternion information. Unlike the current quaternion interpolation methods in the literature, we implement the spline method under the angular velocity constraint in order to interpolate the quaternions from the derived Euler angles so that to obtain more accurate quaternions information in the desired time interval.